Mathematical models have been developed to described hormone-receptor interactions in complex cases involving heterogeneity of hormone and receptor, positive and/or negative cooperativity, and failure to achieve equilibrium or steady-state conditions. By use of computer simulations and curve-fitting techniques, we have derived rate constants and equilibrium constants for binding of human and bovine growth hormones, and of ovine prolactin to rat hepatocytes under a variety of physiological conditions; binding of catecholamines and their synthetic analogs to erythrocytes and erythrocyte membranes; and binding of hCG to rat Leydig cells. A new method has been developed which can, at least in principle, permit calculation of affinity constants, binding capacities, and allow construction of Scatchard plots, without the use of radioisotopes. The effect of factors such as thresholds, spare receptors, and cooperativity on the shape of dose response curves has been analyzed by simulation techniques.